Assignment 12

Cluster3D <- read.arff("Cluster3D.arff")

ggplot(data = Cluster3D, aes(x = x, y = y)) +
  geom_point()

ggplot(data = Cluster3D, aes(x = x, y = z)) +
  geom_point()

ggplot(data = Cluster3D, aes(x = y, y = z)) +
  geom_point()

attach(Cluster3D)
scatterplot3d::scatterplot3d(x = x, y = y, z = z)

plotly::plot_ly(x = x, y = y, z = z, type="scatter3d")

## No scatter3d mode specifed:
##   Setting the mode to markers
##   Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode

## Warning: `arrange_()` is deprecated as of dplyr 0.7.0.
## Please use `arrange()` instead.
## See vignette('programming') for more help
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_warnings()` to see where this warning was generated.

m <- Cluster3D
N <- nrow(m)
K <- matrix(0, nrow=N, ncol=N)
for (i in 1:N) {
  distances <- apply(m, 1, function(r) sum((r - m[i,])^2))
  closest_4 <- order(distances)[2:5]
  K[i,closest_4] <- exp(-distances[closest_4]/.1)
  K[closest_4,i] <- exp(-distances[closest_4]/.1)
}


# create D and A
D <- diag(rowSums(K))/sum(K)
A <- apply(K, 1, function(r) r/sum(r)) %>% t

# create symmetric matrix
S <- D^{1/2} %*% A %*% solve(D^{1/2})

# compute eigenvalues and grab first three
eig.out <- eigen(S)
ind <- order(eig.out$values %>% abs, decreasing = T)
q <- eig.out$vectors[,ind][,1:3]
lambdas <- eig.out$values[ind][1:3]

r <- solve(D^{1/2}) %*% q

# let's just check r1 and lambda1 
#r[,1]
#lambdas[1]



# 2-d projection
t_vals <- c(1,1000, 10000)
for (t in t_vals) {
  y <- cbind(lambdas[2]^t*r[,2], lambdas[3]^t*r[,3])
  g <- ggplot(data=data.frame(y1=y[,1], y2=y[,2])) +
    geom_point(aes(x=y1, y=y2)) +
    xlim(-2,2) + ylim(-2,2) + ggtitle(paste("time", t))
  print(g)
}

knn <- kmeans(x = y, centers = 4)

rm(y)
Cluster3D$assignment <- as.factor(knn$cluster)

ggplot(Cluster3D, aes(x = y, y = z, color = assignment)) +
  geom_point()

attach(Cluster3D)

## The following objects are masked from Cluster3D (pos = 3):
## 
##     x, y, z

plotly::plot_ly(data = Cluster3D, x = x, y = y, z = z, type="scatter3d", color = assignment)

## No scatter3d mode specifed:
##   Setting the mode to markers
##   Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode